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Multiple-Precision Scaled Vector Addition on Graphics Processing Unit

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Parallel Computing Technologies (PaCT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11657))

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Abstract

Many large problems need linear algebra operations with a precision exceeding the standard floating-point binary64 format. In this paper, we implement a multiple-precision scaled vector addition BLAS routine (WAXPBY) on graphics processing units. We use a residue number system (RNS) to represent significands of floating-point values. In RNS, large numbers replace with their residues and the operations of addition, subtraction and multiplication perform on these residues in parallel and without carry propagation. Our parallel WAXPBY algorithm is divided into a number of steps, and each step is carried out by a separate GPU kernel. Experiments show that the developed routine clearly outperforms parallel CPU-based multiple-precision implementations.

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Acknowledgement

This work was supported by the Russian Science Foundation (grant number 18-71-00063).

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Authors and Affiliations

  1. Vyatka State University, Kirov, 610000, Russia

    Konstantin Isupov & Alexander Kuvaev

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  1. Konstantin Isupov
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  2. Alexander Kuvaev
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Correspondence to Konstantin Isupov .

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Editors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk State University, Novosibirsk State Technical University, Novosibirsk, Russia

    Victor Malyshkin

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Isupov, K., Kuvaev, A. (2019). Multiple-Precision Scaled Vector Addition on Graphics Processing Unit. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2019. Lecture Notes in Computer Science(), vol 11657. Springer, Cham. https://doi.org/10.1007/978-3-030-25636-4_14

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  • DOI: https://doi.org/10.1007/978-3-030-25636-4_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25635-7

  • Online ISBN: 978-3-030-25636-4

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